He also has received poor marks for his performance in the CNN Facebook Democratic presidential debate Tuesday night, including an answer in which he explained his 1999 Senate vote to repeal the Glass-Steagall act as coming because "I had just arrived in the Senate."

Chafee on Wednesday blamed his poor performance on his limited speaking time. He spoke for a total of nine minutes in the two-hour debate.

When pushed to discuss what it would take for him to drop out of the race, Chafee said that he would stay in it "as far as I can continue to raise these issues."

"The establishment just does not want to hear an anti-war voice," Chafee said. "And that motivates me even more to continue this campaign." The Middle East is particularly important to him. "Something's going on with what's happening in the Middle East and we need to fix it."

Chafee polled at less than 0.5% percent in a CBS News poll released Sunday.